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Note: Each chapter includes an Algebra Review, Chapter Summary, Study | |
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Strategies, Review Exercises, and Sample Post-Graduation Exam Questions | |
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A Precalculus Review | |
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The Real Number Line and Order | |
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Absolute Value and Distance on the Real Number Line | |
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Exponents and Radicals | |
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Factoring Polynomials | |
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Fractions and Rationalization | |
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Functions, Graphs, and Limits | |
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The Cartesian Plane and the Distance Formula | |
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Graphs of Equations | |
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Lines in the Plane and Slope | |
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Functions | |
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Limits | |
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Continuity | |
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Differentiation | |
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The Derivative and the Slope of a Graph | |
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Some Rules for Differentiation | |
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Rates of Change: Velocity and Marginals | |
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The Product and Quotient Rules | |
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The Chain Rule | |
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Higher-Order Derivatives | |
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Implicit Differentiation | |
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Related Rates | |
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Applications of the Derivative | |
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Increasing and Decreasing Functions | |
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Extrema and the First-Derivative Test | |
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Concavity and the Second-Derivative Test | |
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Optimization Problems | |
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Business and Economics Applications | |
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Asymptotes | |
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Curve Sketching: A Summary | |
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Differentials and Marginal Analysis | |
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Exponential and Logarithmic Functions | |
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Exponential Functions | |
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Natural Exponential Functions | |
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Derivatives of Exponential Functions | |
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Logarithmic Functions | |
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Derivatives of Logarithmic Functions | |
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Exponential Growth and Decay | |
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Integration and Its Applications | |
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Antiderivatives and Indefinite Integrals | |
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The General Power Rule | |
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Exponential and Logarithmic Integrals | |
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Area and the Fundamental Theorem of Calculus | |
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The Area of a Region Bounded by Two Graphs | |
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The Definite Integral as the Limit of a Sum | |
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Volumes of Solids of Revolution | |
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Techniques of Integration | |
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Integration by Substitution | |
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Integration by Parts and Present Value | |
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Partial Fractions and Logistic Growth | |
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Integration Tables and Completing the Square | |
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Numerical Integration | |
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Improper Integrals | |
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Functions of Several Variables | |
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The Three-Dimensional Coordinate System | |
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Surfaces in Space | |
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Functions of Several Variables | |
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Partial Derivatives | |
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Extrema of Functions of Two Variables | |
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Lagrange Multipliers | |
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Least Squares Regression Analysis | |
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Double Integrals and Area in the Plane | |
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Applications of Double Integrals | |
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Trigonometric Functions | |
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Radian Measure of Angles | |
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The Trigonometric Functions | |
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Graphs of Trigonometric Functions | |
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Derivatives of Trigonometric Functions | |
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Integrals of Trigonometric Functions | |
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L'Hocirc;pital's Rule | |
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Probability and Calculus | |
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Discrete Probability | |
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Continuous Random Variables | |
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Expected Value and Variance | |
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Series and Taylor Polynomials | |
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Sequences | |
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Series and Convergence | |
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p-Series and the Ratio Test | |
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Power Series and Taylor's Theorem | |
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Taylor Polynomials | |
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Newton's Method | |
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Appendices | |
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Alternate Introduction to the Fundamental Theorem of Calculus | |
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Formulas | |
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Differentiation and Integration Formulas | |
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Formulas from Business and Finance | |
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Differential Equations | |
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Solutions of Differential Equations | |
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Separation of Variables | |
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First-Order Linear Differential Equations | |
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Applications of Differential Equations The following Appendices available at the text-specific website at college.hmco.com: | |
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Properties of Measurement | |
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Review of Algebra, Geometry, and Trigonometry | |
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Units of Measurement | |
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Graphing Utility Programs | |
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Graphing Utility Programs | |